Measurement and correction of gradient-induced cross-term magnetic fields in an EPI sequence

ABSTRACT

A method is disclosed for determining a gradient-induced cross-term magnetic field in a magnetic resonance imaging (MRI) system involving the steps of: positioning an object in a static magnetic field; applying a radio frequency (RF) excitation pulse that spatially selects a slice of the object; applying an incremented phase-encoding magnetic gradient field along a phase encoding gradient field direction parallel to the slice phase; applying a selective RF refocusing pulse to select a line in the slice; applying a switched readout magnetic gradient; which causes a cross-term magnetic field, generating a data array of a phase-encoding gradient and a corresponding sample data point along the selected line, and determining a center frequency distribution (CF) for the selected line, where the CFR is indicative of a gradient-induced cross-term magnetic field.

BACKGROUND OF THE INVENTION

[0001] The invention relates to magnetic resonance imaging (MRI), and inparticular to high speed echo-planer imaging (EPI) techniques.

[0002] EPI is a commonly used MRI technique for high speed acquisitionof NMR data, in which scan times are generally about 100 msec. For thesimplicity of discussion, the Z-axis is used as the slice selectiondirection, the X-axis is used as the phase-encoding direction, and theY-axis is used as the readout direction. However, other orientations maybe applied when using the invention described herein.

[0003] As shown in FIGS. 1 and 2, in a conventional EPI pulse sequence,a 90° radio frequency (RF) excitation pulse 10 with a slice selectivemagnetic field gradient (G_(slice)) 12 is applied along an axisperpendicular to the imaging plane, e.g., (G_(z)), to excite the nucleiin the imaging plane of the body being imaged. A phase encoding gradient(G_(phase)) 14 and 24 is applied, along an axis (G_(x)) parallel to theimaging plane, after the excitation pulse to spatially encode thenuclei. Similarly, a phase shift gradient (G_(read)) 16 is applied,along an axis (G_(y)) parallel to the imaging plane and orthogonal tothe phase encoding gradient, to center the subsequent scanning of thek-space (raw data space). A 180° RF rephasing pulse 18 is applied togenerate a spin echo (SE) response (ADC) 20 from the excited nuclei. Aslice specific gradient 19 may also be applied in conjunction with the180° RF pulse.

[0004] During a signal sampling period, an alternating readout magneticfield gradient (G_(read)) 22 is applied to scan k-space and acquire SEsignal samples 20 from the excited nuclei. In combination with thereadout gradient, a continuous phase encoding gradient (G_(phase)) 24may be applied to cause the scanning to move along the phase encoding(G_(x)) direction, as is shown in FIG. 3. The scan trajectory 26 forms azig-zag pattern through k-space due to the alternating readout gradient22 and the continuous phase encoding gradient 24. Alternatively, thephase encoding gradient may be applied as blip pulses 28 aligned withthe reversal of the readout gradient to shift the scan trajectory 30after each pass through a row of k-space, as is shown in FIG. 4.

[0005] As is shown in FIGS. 3 and 4, data is generally sampled during anEPI sequence in a raster scan trajectory through k-space, whereindividual scan lines corresponding to the readout gradient aresequentially sampled. After each scan line 32 is sampled, the k-spacetrajectory is shifted along the phase gradient direction to a next scanline 34. The reversal of the readout gradient 22 causes the k-spacetrajectory to be reverse along the readout gradient. By reversing thetrajectory, the scan through k-space can proceed back and forth alongthe readout gradient on a line by line sequence.

[0006] The phase encoding gradient 24, 28 is perpendicular to the lineby line trajectory of the data acquisition trajectory. Data along a lineparallel to the phase encoding gradient is acquired slowly during thecourse of an entire scan of k-space. In contrast, data acquired alongeach line parallel to the readout gradient is acquired quickly as thescanning trajectory passes through one line of the scanning trajectory.Accordingly, data in the phase encoding gradient direction is acquiredat a much slower rate than is data collected along the readout gradientdirection.

[0007] The NMR signal samples acquired during the readout gradient maybe transformed from the k-space domain to a spatial domain usingconventional mathematical techniques, such as a Fourier transform. Datain the spatial domain is used to generate a NMR image of a cross-sectionof the body corresponding to the slice selected for imaging.

[0008] Images generated using an EPI sequence are susceptible todistortion and artifacts caused by magnetic field inhomogeneities andother abnormalities of the MRI system. With respect to high speed imagesgenerated using EPI sequences, the image distortions are particularlyacute along the phase encoding direction because of the relatively slowdata sampling rate along that direction.

[0009] Induced magnetic field distortions are a source of imagedistortions. An induced field distortion arises when a magnetic field isinduced by a switched gradient magnetic field in an MR imaging sequence,an EPI sequence. The induced field is a cross-field when it isorthogonal to the inducing gradient field. Induced magnetic cross-fielddistortions may result from eddy-currents (EC) and Maxwellelectromagnetic fields in the MRI system. For example, during an EPIsequence, an induced cross-field may arise along the phase-encodingdirection due to the rapidly switched readout gradient during the datasampling period.

[0010] In view of the relatively slow sampling rate along thephase-encoding direction (G_(phase)), the gradient induced cross-fielddue to a switched readout gradient (G_(read)) may result in substantialimage distortions along the phase-encoding direction. The imagedistortion may be particularly acute in images generated from an EPIsequence where the readout gradient is repeatedly reversed during thedata sampling period. There is a long-felt need for techniques tocompensate for induced magnetic cross-fields that create imagedistortions, especially for distortions resulting from EPI sequencesduring which induced cross-fields are generated by the readout gradient.

BRIEF SUMMARY OF THE INVENTION

[0011] A technique has been developed for compensating for thedistortions in the image data due to induced magnetic cross fields, andespecially those generated by a switched readout gradient. Thecompensation technique allows for distortions in images due to inducedcross-fields to be substantially reduced. The induced cross-fielddistortions are often acute along a direction corresponding to thephase-encoding gradient. The compensation technique is most helpful inreducing image distortion along the phase-encode direction.

[0012] The compensation technique includes initially measuring theinduced magnetic cross-field, preferably by imaging a phantom object.The measurements of the induced cross-field effects in a phantom objectare used to generate a cross-term correction factor. This factor is usedto reduce image distortion and artifacts due to the cross-field inducedduring signal sampling of a patient's body.

[0013] In one embodiment, the invention is a method for determining agradient-induced cross-term magnetic field in a magnetic resonanceimaging (MRI) system involving the steps of: positioning an object in astatic magnetic field; applying a radio frequency (RF) excitation pulsethat spatially selects the nuclei of a slice plane in the object;applying an incremental phase-encoding magnetic gradient field along aphase encoding direction perpendicular to the slice direction; applyingan RF refocusing pulse that is spatially selective along a readoutmagnetic gradient field direction, so as to select nuclei of the objectalong a selected line in said slice plane; sampling nuclear magneticresonance (NMR) from the selected nuclei by applying a readout magneticfield gradient to the object, wherein the readout gradient repeatedlycycles during a sampling period, generating data corresponding to aphase-encoding gradient k-space value at a series of time points insidethe readout duration, and determining a center frequency distribution(CF) along the selected line, where the CF distribution is indicative ofa gradient-induced cross-term magnetic field.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014]FIG. 1 is a sequence diagrams showing a conventional spin-echotwo-dimensional (2D) EPI pulse sequence with a continuous phase-encodinggradient;

[0015]FIG. 2 is a sequence diagram showing a conventional spin-echo 2DEPI pulse sequence with blipped phase-encoding gradient pulses;

[0016]FIG. 3 is a chart showing the k-space trajectories sampled by theEPI sequence with a continuous phase-encoding gradient, as is diagramedin FIG. 1;

[0017]FIG. 4 is a chart showing the k-space trajectories sampled by thestandard EPI sequence with blipped phase-encoding gradient, as isdiagramed in FIG. 2;

[0018]FIG. 5 is a schematic diagram of an MRI system;

[0019]FIG. 6 is a flow diagram showing generally the steps in generatingand applying a cross-term magnetic field correction factor;

[0020]FIG. 7 is a sequence diagram showing a modified EPI pulse sequencefor measuring cross-fields induced by the switched EPI readout gradientpulses, and

[0021]FIG. 8 is a sequence diagram showing another modified EPI pulsesequence for measuring cross-fields induced by the switched EPI readoutgradient pulses.

DETAILED DESCRIPTION OF THE INVENTION

[0022] As shown in FIG. 5, an MR imaging system 40 typically includes amagnet 42 to impose a static magnetic field (B₀), gradient coils 44 forimposing spatially distributed gradient magnetic fields (G_(x), G_(y),and G_(z)) having gradients along three respective orthogonalcoordinates, and RF coils 46 to transmit and receive RF signals to andfrom the selected nuclei of the body being imaged. The patient 48 lieson a patient table 50 such that a portion of the patient to be imaged isin an “imaging volume” between the magnet and coils, which defines afield of view (FOV) of the MRI system.

[0023] The electromagnetic fields generated by the operation of thegradient coils 44 may induce cross-fields in the imaging volume. Themagnitude of the induced cross-fields is dependent on the switching ofgradient coils and the current in the coils. The induced cross-fieldsmay be relatively large while gradient coils are rapidly switched, suchas when the polarity of the readout gradient (G_(read)) is repeatedlyreversed during a signal sampling period of an echo planar imaging (EPI)sequence. The induced cross-fields act on the phasing of the nuclei ofthe body in the imaging volume and thereby influence the NMR signalscollected for MR imaging.

[0024]FIG. 6 is a chart of a method for generating a cross-term fieldcorrection factor. The method corrects for induced cross-term magneticfields, and particularly those caused by switched readout gradients. Toisolate the effects on NMR signal data, a phantom sample is positionedat the iso-center 52 of the imaging volume, in step 54. The phantomsample may be a vessel filled with a hydrogen-rich fluid, such as babyoil. One example of a phantom sample is a 10 cm×10 cm×30 cm rectangularcolumn vessel filled with baby-oil. The phantom object is imaged withthe same EPI sequence as will be later used to image a patient. Inparticular, the phantom object may be imaged with an EPI sequence usingthe same readout gradient reversal rate and sampling period as is to belater used when imaging the patient.

[0025] The measurement of the cross-term may be made using an excitationline technique 58 or a saturation line technique 60. Moreover, theexcitation line technique 58 may be implemented as a one-line excitation62, wherein only the cross-term is measured, or a two line excitation64, where both the cross-term and the readout gradient trajectory timingare measured 66. The one and two-line excitation and the line saturationtechniques each generate data from which a cross-term field correctionfactor (B_(I)(Y)) 68 is generated.

[0026] The correction factor (B_(I)(y)) is later applied to correctimage data collected when scanning a patient. It is assumed that theinduced cross-term that arises with the phantom sample is substantiallythe same as the induced cross-term that will arise when a patient isbeing imaged. Thus, the correction factor B_(I)(y)) generated using thephantom sample is applicable to correct for the cross-term in image dataof a patient. The correction factor (B_(I)(Y)) 68 is the used tocorrect, using a conventional image correction algorithm 70, the rawimaging data 72 collected from an EPI scan of a patient. The imagegenerated 73 using the corrected raw image data should be largely freeof artifacts due to the induced cross-term magnetic fields.

[0027]FIG. 7 shows a modified spin-echo EPI sequence 74 for measuringcross-fields induced by a switched EPI readout gradient pulses. Themodified sequence 74 includes: a 90° degree RF excitation pulse 76spatially selective, with a slice selection gradient 78 pulse along theslice direction; a 180° degree RF refocusing pulse 80 spatiallyselective along the readout direction; an incremented phase-encodinggradient 89 applied between the 90° and 180° RF pulses, and a switchedEPI readout gradient 84 alternating between positive and negativepolarities is applied during the acquisition of the NMR signals (ADC)86. The readout gradient pulses may be the same as in regular EPIimaging application of patients.

[0028] The modified EPI sequence 74 is used to acquire the NMR signaldata used to determine the cross-fields induced by the EPI readoutgradient pulses 84. A slice of the phantom object is selected by thespatially selective 90° pulse 76 in the presence of the slice gradient78. Subsequently, a line from the slice is selected by the spatiallyselective 180° RF pulse 80 applied in the presence of a gradient 88along the readout direction. Preferably, the selected line may be thickalong the slice direction, e.g., about 1 cm (centimeters), and thinalong the readout direction, e.g., in a range of about 2 to 3 mm(millimeters). The selected straight line is phase encoded with anincremented phase-encoding gradient pulse 89 along the direction of theline. The phase encoding spatially encodes the selected line.

[0029] The NMR signals acquired from the selected line evidence theeffects of the cross-fields induced by the EPI switched readoutgradients. Since a straight line is selected and a phantom sample isbeing imaged, the variations of the NMR frequency along the line areattributable to the cross-fields induced by the switched EPI readoutgradient pulses.

[0030] The excitation line method 58 may be used to measure the inducedmagnetic cross-fields only, or both the cross-fields and the EPI readoutgradient trajectories. To measure only the induced magneticcross-fields, a single line is selected that passes through theiso-center of the MRI system. The line(s) is selected along thedirection, e.g. G_(phase), for which the cross-fields are to be measuredand the readout is along the direction of the inducing gradient pulses,e.g., G_(read).

[0031] The measurement yields a data array represented by S(k_(m),t_(n)), where m=1, 2, . . . , M, and n=1, 2, . . . , N. In this dataarray, k_(m) is the phase-encoding gradient k-value; t_(n) representsthe time when the data point is acquired within the EPI readout window,and M and N are the number of data points acquired along thephase-encoding and readout dimensions, respectively. The data arrayS(k_(m), t_(n)) contains the information of the distortion of NMRsignals due to the cross-magnetic fields induced by a gradient field,such as a switched EPI readout gradient.

[0032] If both the trajectory of the EPI readout gradient and thecross-fields induced by the readout gradient are to be measured, thentwo parallel lines 64 are selected for acquisition of twin data arrays.The lines are equally offset but in opposite directions from theiso-center along the readout direction by +L and −L, respectively. Thelines are parallel to the direction of the cross-term, e.g. G_(phase).The measurement of the NRM data along the two selected lines yields twodata arrays, S^(+L)(k_(m), t_(n)) and S^(−L)(k_(m), t_(n)), with eacharray corresponding to one of the selected lines.

[0033] The acquired data from each line are first one-dimensional (1D)Fourier transformed (FT) along the phase-encoding direction, and thensubjected to further processing steps for measuring the EPI readoutgradient trajectory and the cross-fields induced by the EPI readoutgradient.

[0034] For measurement of the EPI readout gradient trajectory, after the1D FT along the phase-encoding direction, the instantaneous frequencyf(Y_(m),t_(n)) corresponding to position Y_(m) and time t_(n), isdetermined from the signal phases in accordance with equation 1 below:$\begin{matrix}{{f\left( {Y_{m},t_{n}} \right)} = \frac{\arg \left\{ {{S\left( {Y_{m},t_{n}} \right)} \cdot {S^{*}\left( {Y_{m},t_{n - 1}} \right)}} \right\}}{t_{n} - t_{n - 1}}} & \lbrack 1\rbrack\end{matrix}$

[0035] where S^(*)(Y_(m),t_(n−1)) is the conjugate of S(Y_(m),t_(n−1))and arg{ } returns the principal phase value of its complex input.

[0036] The gradient trajectory is determined from the instantaneousfrequencies according to equation 2: $\begin{matrix}{{k\left( t_{n} \right)} = {\frac{1}{M}{\sum\limits_{m = 1}^{M}\quad \frac{{f^{+ L}\left( {Y_{m},t_{n}} \right)} - {f^{- L}\left( {Y_{m},t_{n}} \right)}}{2L}}}} & \lbrack 2\rbrack\end{matrix}$

[0037] where f(Y_(m),t_(n)) is the instantaneous frequency at positionY_(m) and time t_(n) when each data point is acquired along a selectedline, and L (+ and −) are the offsets of the selected line from theiso-center.

[0038] To determine the cross-fields induced by the EPI readoutgradient, a reduced array of data representative of the cross-field isextracted from the measured data array as shown in equation 3:

S(Y _(m) ,t _(p))εS(Y _(m) ,t _(n))  [3]

[0039] where t_(p) represents the time when the corresponding point inthe reduced data array is acquired.

[0040] The sub-array S(Y_(m), t_(p)) is extracted by taking the centerpoint from each EPI echo. If both even and odd echoes are used inproducing EPI images, the sub-array may consist of data representativeof the echo center points of the complete EPI echo train.

[0041] The instantaneous frequency (f (Y_(m), t_(p))) is againcalculated according to equation [1], but using the reduced arrayinstead as represented by equation 4: $\begin{matrix}{{f\left( {Y_{m},t_{p}} \right)} = \frac{\arg \left\{ {{S\left( {Y_{m},t_{p}} \right)} \cdot {S^{*}\left( {Y_{m},t_{p - 1}} \right)}} \right\}}{t_{p} - t_{p - 1}}} & \lbrack 4\rbrack\end{matrix}$

[0042] In the case of a single-line measurement 62, the instantaneousfrequency, after 1D FT of f (Y_(m), t_(p)) to yield CF(Y_(m)), may bedirectly used and fitted to a polynomial function of Y_(m) usingalgorithms such as the least square minimization. The polynomialfunction from the fitting represents the center frequency distribution,CF(Y_(m)) along the selected line, which is in the direction ofmeasurement for cross-field distribution. The center frequencydistribution is related to the induced cross-field byγB₁(Y_(m))=CF(Y_(m)), where B₁ stands for the induced cross-field.

[0043] In the case of the double-line measurement 64, when the gradienttrajectory is also to be measured, the addition of the instantaneousfrequencies from the two symmetrically shifted lines are used and fittedto a polynomial function of Y_(m), again after 1D FT of f⁺(Y_(m),t_(p))to yield CF(Y_(m)), to determine a center frequency distribution(CF(Y_(m))) using equation 5, as follows: $\begin{matrix}{{f^{+}\left( {Y_{m},t_{p}} \right)} = \frac{{f^{L}\left( {Y_{m},t_{p}} \right)} + {f^{- L}\left( {Y_{m},t_{p}} \right)}}{2}} & \lbrack 5\rbrack\end{matrix}$

[0044]FIG. 8 shows another modified spin-echo EPI sequence 90 formeasuring cross-fields induced by the switched EPI readout gradientpulses. The sequence includes a 90° RF excitation pulse 92 and gradient94 that are spatially selective along both the phase-encoding directionand readout direction for selectively saturating a slice of spins angledin-between the phase-encoding direction and readout direction. After thefirst 90° RF pulse 92, a standard spin-echo EPI sequence 96 is applied,which includes another 90° RF pulse 98. The spatial distribution of thesaturated slice, which shows as a dark line in the acquired 2D EPIimage, is indicative of the induced cross-fields. The phase-encodingposition displacement ΔX_(m) as a function of the phase encodingposition ΔX_(m)(X_(m)) may be fitted to a polynomial function forquantifying the cross-fields.

[0045] The procedures for data acquisition and processing may berepeated for various line orientations and with as many variations ofEPI readout gradient waveforms as are needed to model the inducedmagnetic cross-fields for the operating modes used by the MRI system toimage patients. Further, these procedures may be part of a systemcalibration package that is applied to characterize an MRI scanner. Theresults of these procedures may be stored as part of the systemspecification parameters. The results of these procedures may be appliedto correct images, or make system adjustments necessary to reduce imagedistortion or artifacts caused by the cross-fields.

[0046] The cross-fields induced by the EPI readout gradient aremanifested into image distortions along the phase-encoding direction thesame way as do static field inhomogeneities. Accordingly, the resultsfrom cross-field measurement are used for image correction by applyingthe same algorithm as for B₀ inhomogeneity correction. Examples of B₀inhomogeneity correction algorithms are set forth in: Chang, H., andFitzpatrick, J. M., “A Technique for Accurate Magnetic Resonance Imagingin the Presence of Field Inhomogeneities”, IEEE Transactions on MedicalImaging 11:319-329, 1992; O'Donnell M., and Edelstein, W. A., “NMRImaging in the Presence of Magnetic Field Inhomogeneities and GradientField Nonlinearities”, Med. Phys. 12:20-26, 1985; Sekihara, K., Matsui,S., and Kohno, H., “NMR Imaging for Magnets with Large Nonuniformities”,IEEE Transactions on Medical Imaging MI-4:193-199, 1985. Theinhomogeneity correction procedures may be applied with cross-termcorrections for reducing EPI image distortion.

[0047] While the invention has been described in connection with what ispresently considered to be the most practical and preferred embodiment,it is to be understood that the invention is not to be limited to thedisclosed embodiment, but on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

What is claimed is:
 1. A method for determining a gradient-inducedcross-term magnetic field in a magnetic resonance imaging (MRI) systemcomprising: a. positioning an object in a static magnetic field; b.applying a radio frequency (RF) excitation pulse that spatially selectsnuclei of a slice of the object in a slice plane; c. applying anincremented phase-encoding magnetic gradient field along a phaseencoding gradient field direction parallel to the slice plane; d.applying a spatially selective RF refocusing pulse along a readoutmagnetic gradient field direction to select an encoded line in saidslice plane; e. sampling nuclear magnetic resonance (NMR) data fromnuclei in the selected line by applying a switched readout magneticgradient to the object, wherein the switched readout gradient generatesa cross-term magnetic field with respect to said object; f. transformingthe sampled NMR data into an array of data representative of thecross-field effects along the phase encoding gradient field direction,and g. determining a cross term correction factor for the selected linebased on the array of data.
 2. A method as in claim 1 wherein the objectis aligned with an iso-center of the readout gradient field.
 3. A methodas in claim 1 wherein the object is a phantom sample vessel containing ahydrogen rich fluid.
 4. A method as in claim 1 performed whilecalibrating the MRI system.
 5. a method as in claim 1 wherein theexcitation pulse is a 90° RF pulse and a slice selective magneticgradient field perpendicular to a plane of the slice.
 6. A method as inclaim 1 wherein the incremented phase-encoding gradient field is appliedno earlier than the excitation pulse and no later than the refocusingpulse.
 7. A method as in claim 1 wherein the incremented phase encodingmagnetic gradient field phase encodes nuclei in the object along the eselected line so nuclear magnetic resonance (NMR) signals generated bysaid encoded nuclei are encoded incrementally along said line forspatial resolution.
 8. A method as in claim 1 wherein the readoutdirection is in the slice plane and is orthogonal to the phase encodinggradient field direction.
 9. A method as in claim 1 wherein the selectedline has a width of no greater than three millimeters along the readoutgradient.
 10. A method as in claim 1 wherein the selected line is at theiso-center of the magnet.
 11. A method as in claim 1 wherein theselected line is a first selected line offset along the readoutdirection by a distance from the iso-center, and wherein a secondselected line of nuclei is spatially selected along the readoutdirection and offset from the iso-center by a distance L in a directionopposite to the offset of the first selected line.
 12. A method as inclaim 10 wherein the array of data is arranged in an array representedby S(k_(m), t_(n)) where m=1, 2, . . . , M, and n=1, 2, . . . , N; k_(m)is a phase-encoding gradient k-value; t_(n) represents a time when eachdata point is acquired, and M and N indicate an number of data pointsacquired along the phase-encoding and readout dimensions, respectively.13. A method as in claim 11 wherein the generated data is arranged intwin data arrays, S^(+L)(k_(m), t_(n)) and S^(−L)(k_(m), t_(n)) eachcorresponding to one of the first and second selected lines, and wherem=1, 2, . . . , M, and n=1, 2, . . . , N; k_(m) is a phase-encodinggradient k-value; t_(n) represents a time when each data point isacquired, and M and N indicate a number of data points acquired alongthe phase-encoding and readout dimensions, respectively.
 14. A method asin claim 12 wherein a readout gradient trajectory is determined byapplying a one-dimensional Fourier transformation to the twin dataarrays, and further comprising determining an instantaneous frequency(f) at each readout position (t_(n)) as follows:${f\left( {Y_{m},t_{n}} \right)} = \frac{\arg \left\{ {{S\left( {Y_{m},t_{n}} \right)} \cdot {S^{*}\left( {Y_{m},t_{n - 1}} \right)}} \right\}}{t_{n} - t_{n - 1}}$

where f(Y_(m), t_(n)) is the instantaneous frequency at position Y_(m)and time t_(n) when each data point is acquired along the selected line,S*(Y_(m),t_(n−1)) is a conjugate of S(Y_(m),t_(n−1)) and arg{ } returnsa principal phase value for a complex input.
 15. A method as in claim 13wherein a readout gradient trajectory (k(t_(n))) is determined from theinstantaneous frequencies (f) according to the following equation:${k\left( t_{n} \right)} = {\frac{1}{M}{\sum\limits_{m = 1}^{M}\quad \frac{{f^{+ L}\left( {Y_{m},t_{n}} \right)} - {f^{- L}\left( {Y_{m},t_{n}} \right)}}{2L}}}$

where f^(+L) (Y_(m)t_(n)) is a function of instantaneous frequenciescorresponding to the first selected line and f^(−L) (Y_(m)t_(n)) is afunction of instantaneous frequencies corresponding to the secondselected line, and L is an offset distance of the selected line from theiso-center.
 16. A method as in claim 12 wherein the cross-fieldcorrection factor CF(Ym) is determined from a reduced data set: S(Y_(m),t_(p))εS(Y_(m), t_(n)).
 17. A method as in claim 16 wherein thecross-field correction factor is CF(Y_(m)) which is determined as aFourier transform of a frequency distribution f(Y_(m)T_(n)) determinedaccording to:${f\left( {Y_{m},t_{p}} \right)} = {\frac{\arg \left\{ {{S\left( {Y_{m},t_{p}} \right)} \cdot {S^{*}\left( {Y_{m},t_{p - 1}} \right)}} \right\}}{t_{p} - t_{p - 1}}.}$


18. A method as in claim 13 wherein the cross-field correction factor isf (Y_(m)) and is determined as is Fourier transform of the averagefrequency distribution that is determined according to:${f^{+}\left( {Y_{m},t_{p}} \right)} = \frac{{f^{L}\left( {Y_{m},t_{p}} \right)} + {f^{- L}\left( {Y_{m},t_{p}} \right)}}{2}$

where f^(L) (Y_(m), t_(p)) and f^(−L) (Y_(m), t_(p)) are instantaneousfrequencies of the two symmetric lines offset by a distance L from aniso-center of the magnet.
 19. A method as claim 1 wherein thecross-field correction factor is applied to correct an image of a secondobject and reduce image distortion in the image due to a cross-termmagnetic field induced by the EPI readout gradient pulse.
 20. A methodfor determining a gradient-induced cross-term magnetic field in amagnetic resonance imaging (MRI) system comprising: a. positioning anobject in a static magnetic field; b. applying a radio frequency (RF)saturation pulse that spatially saturates nuclei of a slice of theobject, and c. after step (b), applying an echo planar imaging (EPI)sequence to form an image of a slice of the object.
 21. A method as inclaim 20 wherein the RF saturation slice is oriented in-between areadout direction and a phase-encoding direction of the EPI sequence.22. A method as in claim 20 wherein the RF saturation slice appears as adark saturation line in the image generated in step (c), and furthercomprising a step (d) of analyzing a spatial distribution of thesaturation line to yield a cross-field correction factor.
 23. A methodas claim 20 further comprising: e. generating a cross-field correctionfactor using the image of the slice of the object, and f. applying thecross-field correction factor to correct another image of a secondobjection and thereby reduce image distortion due to a cross-termmagnetic field induced by the EPI readout gradient pulse.